Generalizing Tree Probability Estimation via Bayesian Networks

2018/05/20 by Cheng Zhang, F. A. Matsen, Zhang, Cheng +1 · 1 citation
Computer Science · #Applications (stat.AP) #Bayesian Modeling and Causal Inference #Data Management and Algorithms #FOS: Computer and information sciences #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.1805.07834

openalex publication_date 2018/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we derive a general Bayesian network formulation for probability estimation on leaf-labeled trees that enables flexible approximations which can generalize beyond observations. We show that efficient algorithms for learning Bayesian networks can be easily extended to probability estimation on this challenging structured space. Experiments on both synthetic and real data show that our methods greatly outperform the current practice of using the empirical distribution, as well as a previous effort for probability estimation on trees.

Citations

• Bayesian Phylogenetic Inference via Markov Chain Monte Carlo Methods
• Gradient-based learning applied to document recognition
• MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space
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Cited by

• Bayesian credible sets for phylogenetic tree topologies with applications to coverage analysis and cross-model comparison

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